Question

In the circuit shown, the current through the $5\,\Omega$ resistor is

• A. $\frac{8}{3}A$
• B. $\frac{9}{13}A$
• C. $\frac{4}{13}A$
• D. $\frac{1}{3}A$

Answer 1

Answer: (D)

$\frac{1}{3}A$

Answer 2

$\frac{1}{R}=\frac{1}{2}+\frac{1}{2}=1$
$R=1\,\Omega$ Total resistance
$=R+5=1+5=6\,\Omega$
${{E}_{eff}}=\frac{{{E}_{1}}{{r}_{1}}+{{E}_{2}}{{r}_{2}}}{{{r}_{1}}+{{r}_{2}}}=\frac{2\times 2+2\times 2}{2+2}$
$=2\,V$
$i=\frac{{{E}_{ff}}}{R}=\frac{2}{6}=\frac{1}{3}A$